A154118 Expansion of (1 - x + 5x^2)/((1-x)*(1-2x)).

1, 2, 9, 23, 51, 107, 219, 443, 891, 1787, 3579, 7163, 14331, 28667, 57339, 114683, 229371, 458747, 917499, 1835003, 3670011, 7340027, 14680059, 29360123, 58720251, 117440507, 234881019, 469762043, 939524091, 1879048187, 3758096379, 7516192763, 15032385531

Offset: 0

Author

Philippe Deléham, Jan 05 2009

Keywords

• nonn
• easy
• less

Comments

Binomial transform of 1,1,6,1,6,1,6,1,6,1,6,1,6,1,6,...

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

Mathematica

Join[{1},Table[7*2^(n-1)-5,{n,15}]] (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011*)
Join[{1, 2, 9}, LinearRecurrence[{3, -2}, {23, 51}, 20]] (* G. C. Greubel, Sep 02 2016 *)

PARI

a(n)=if(n,7<<(n-1)-5,1) \\ Charles R Greathouse IV, Jan 17 2012

Formula

a(n) = 7*2^(n-1) - 5, n>=1, with a(0)=1.

a(n) = 2*a(n-1) + 5, n>1, with a(0)=1, a(1)=2.

a(n) = 3*a(n-1) - 2*a(n-2), n>2, with a(0)=1, a(1)=2, a(2)=9.

E.g.f.: (1/2)*(5 - 10*exp(x) + 7*exp(2*x)). - G. C. Greubel, Sep 02 2016